States that fully embraced the coverage expansion under President Barack Obama’s health care law are experiencing a significant drop in the share of their residents who remain uninsured, according to an extensive new poll released Tuesday.

WASHINGTON — President Barack Obama’s health care law has become a tale of two Americas.

States that fully embraced the law’s coverage expansion are experiencing a significant drop in the number of uninsured residents, according to a major new survey released Tuesday. States whose leaders still object to “Obamacare” are seeing much less change.

The Gallup-Healthways Well-Being Index found an overall drop of 4 percentage points in the share of uninsured residents for states accepting the law’s core coverage provisions. Those are states that expanded their Medicaid programs and also built or took an active role managing new online insurance markets.

The drop was about half that level — 2.2 percentage points — in states that took neither of those steps, or just one of them.

“Those states that implement the law’s major mechanisms are seeing a significantly greater decline in their uninsured rates,” said Dan Witters, research director for the poll.

Medicaid expansion mainly helps low-income uninsured adults in states accepting it. Insurance exchanges operate in every state, offering taxpayer-subsidized private coverage to people who have no health plan on the job.

Leading the nation were two southern states where the law has found political support. Arkansas saw a drop of about 10 percentage points in its share of uninsured residents, from 22.5 percent in 2013, to 12.4 percent by the middle of this year. Kentucky experienced a drop of nearly 9 percentage points, from 20.4 percent of its residents uninsured in 2013, to 11.9 percent.

Although the poll’s margin of sampling error is higher for smaller states, Witters said Gallup has a high level of confidence that the numbers represent real changes.

The poll found contrasts among states that share a border, but have taken different paths politically on the health care law.

— While Arkansas had the 10-point decline in its uninsured rate, the drop in Tennessee was just 2.4 percentage points.

— The uninsured rate in West Virginia fell 5.7 points after the state agreed to Medicaid expansion, but there was no change for neighboring Virginia, where Democratic Gov. Terry McAuliffe has been blocked by a Republican-led legislature.

— Colorado’s uninsured rate dropped 6 percentage points with Medicaid expansion and a state-run exchange, while Utah’s didn’t budge. That state has a federally-run exchange and is still weighing whether to expand Medicaid.

It’s unclear if emerging disparities among neighboring states will start to shift the hardened lines in the political debate over health care. Americans remain divided over Obama’s signature program, with opponents clearly outnumbering supporters.

Robert Blendon, a public opinion analyst at the Harvard School of Public Health, said immediate shifts are unlikely. That’s because negative views about the law are driven by people who already had insurance. They worry that the coverage expansion will raise their premiums or compromise the quality of care they receive.

“Why isn’t the bill more popular?” asked Blendon. “Rightly or wrongly, people who are not directly aided by it are worried.”